Solar Power Plant EDA & Irradiation Predictor
Jasmine Samuel
9/3/2020
We are going to be looking at solar plant energy data. We will rely heavily on EDA for this analysis
We have data from two plants with the same metrics being measured
Let’s define the variables
DATE_TIME: Refers to the date_time in 15 minute intervals
PLANT_ID: Refers to the specific plant ID- there are only two plants that have been sampled
SOURCE_KEY(generator): Refers to the inverter id
SOURCE_KEY(sensor): Sensor panel id
AMBIENT_TEMPERATURE: Temperature at the plant
MODULE_TEMPERATURE: Temperature of the sensor
IRRADIATION: Amount of solar IRRADIATION in 15 minute intervals. Solar irradiation refers to the conversion of solar light to solar energy.
DC_POWER: Amount of direct current power generated in 15 minute intervals
AC_POWER: Amount of alternating current power generated in 15 minute intervals
DAILY_YIELD: Cumulative sum of power generated at that point in the day
TOTAL_YIELD: Total yield for that inverter up until that point
Let’s start by importing relevant packages & reviewing the data
library('ggplot2')
library('dplyr')##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary('olsrr')##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riverslibrary('ggpubr')
library('gridExtra')##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combineReading in the 4 seperate files
plant_g_1 <- read.csv(file.path('/Users/jasminesamuel/Downloads/836676_1428586_bundle_archive/Plant_1_Generation_Data.csv'))
plant_g_2 <- read.csv(file.path('/Users/jasminesamuel/Downloads/836676_1428586_bundle_archive/Plant_2_Generation_Data.csv'))
plant_s_1 <- read.csv(file.path('/Users/jasminesamuel/Downloads/836676_1428586_bundle_archive/Plant_1_Weather_Sensor_Data.csv'))
plant_s_2 <- read.csv(file.path('/Users/jasminesamuel/Downloads/836676_1428586_bundle_archive/Plant_2_Weather_Sensor_Data.csv'))Looking at the data structure and getting familar with the data & variables
str(plant_g_1) # solar plant generator data ## 'data.frame': 68778 obs. of 7 variables:
## $ DATE_TIME : chr "15-05-2020 00:00" "15-05-2020 00:00" "15-05-2020 00:00" "15-05-2020 00:00" ...
## $ PLANT_ID : int 4135001 4135001 4135001 4135001 4135001 4135001 4135001 4135001 4135001 4135001 ...
## $ SOURCE_KEY : chr "1BY6WEcLGh8j5v7" "1IF53ai7Xc0U56Y" "3PZuoBAID5Wc2HD" "7JYdWkrLSPkdwr4" ...
## $ DC_POWER : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AC_POWER : num 0 0 0 0 0 0 0 0 0 0 ...
## $ DAILY_YIELD: num 0 0 0 0 0 0 0 0 0 0 ...
## $ TOTAL_YIELD: num 6259559 6183645 6987759 7602960 7158964 ...str(plant_g_2)## 'data.frame': 67698 obs. of 7 variables:
## $ DATE_TIME : chr "2020-05-15 00:00:00" "2020-05-15 00:00:00" "2020-05-15 00:00:00" "2020-05-15 00:00:00" ...
## $ PLANT_ID : int 4136001 4136001 4136001 4136001 4136001 4136001 4136001 4136001 4136001 4136001 ...
## $ SOURCE_KEY : chr "4UPUqMRk7TRMgml" "81aHJ1q11NBPMrL" "9kRcWv60rDACzjR" "Et9kgGMDl729KT4" ...
## $ DC_POWER : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AC_POWER : num 0 0 0 0 0 0 0 0 0 0 ...
## $ DAILY_YIELD: num 9425 0 3075 270 3177 ...
## $ TOTAL_YIELD: num 2.43e+06 1.22e+09 2.25e+09 1.70e+06 1.99e+07 ...str(plant_s_1) # solar plant sensor data ## 'data.frame': 3182 obs. of 6 variables:
## $ DATE_TIME : chr "2020-05-15 00:00:00" "2020-05-15 00:15:00" "2020-05-15 00:30:00" "2020-05-15 00:45:00" ...
## $ PLANT_ID : int 4135001 4135001 4135001 4135001 4135001 4135001 4135001 4135001 4135001 4135001 ...
## $ SOURCE_KEY : chr "HmiyD2TTLFNqkNe" "HmiyD2TTLFNqkNe" "HmiyD2TTLFNqkNe" "HmiyD2TTLFNqkNe" ...
## $ AMBIENT_TEMPERATURE: num 25.2 25.1 24.9 24.8 24.6 ...
## $ MODULE_TEMPERATURE : num 22.9 22.8 22.6 22.4 22.2 ...
## $ IRRADIATION : num 0 0 0 0 0 0 0 0 0 0 ...str(plant_s_2) # solar plant sensor data ## 'data.frame': 3259 obs. of 6 variables:
## $ DATE_TIME : chr "2020-05-15 00:00:00" "2020-05-15 00:15:00" "2020-05-15 00:30:00" "2020-05-15 00:45:00" ...
## $ PLANT_ID : int 4136001 4136001 4136001 4136001 4136001 4136001 4136001 4136001 4136001 4136001 ...
## $ SOURCE_KEY : chr "iq8k7ZNt4Mwm3w0" "iq8k7ZNt4Mwm3w0" "iq8k7ZNt4Mwm3w0" "iq8k7ZNt4Mwm3w0" ...
## $ AMBIENT_TEMPERATURE: num 27 26.9 26.7 26.5 26.6 ...
## $ MODULE_TEMPERATURE : num 25.1 24.4 24.4 24.4 25.1 ...
## $ IRRADIATION : num 0 0 0 0 0 0 0 0 0 0 ...head(plant_g_1)## DATE_TIME PLANT_ID SOURCE_KEY DC_POWER AC_POWER DAILY_YIELD
## 1 15-05-2020 00:00 4135001 1BY6WEcLGh8j5v7 0 0 0
## 2 15-05-2020 00:00 4135001 1IF53ai7Xc0U56Y 0 0 0
## 3 15-05-2020 00:00 4135001 3PZuoBAID5Wc2HD 0 0 0
## 4 15-05-2020 00:00 4135001 7JYdWkrLSPkdwr4 0 0 0
## 5 15-05-2020 00:00 4135001 McdE0feGgRqW7Ca 0 0 0
## 6 15-05-2020 00:00 4135001 VHMLBKoKgIrUVDU 0 0 0
## TOTAL_YIELD
## 1 6259559
## 2 6183645
## 3 6987759
## 4 7602960
## 5 7158964
## 6 7206408head(plant_g_2)## DATE_TIME PLANT_ID SOURCE_KEY DC_POWER AC_POWER DAILY_YIELD
## 1 2020-05-15 00:00:00 4136001 4UPUqMRk7TRMgml 0 0 9425.0000
## 2 2020-05-15 00:00:00 4136001 81aHJ1q11NBPMrL 0 0 0.0000
## 3 2020-05-15 00:00:00 4136001 9kRcWv60rDACzjR 0 0 3075.3333
## 4 2020-05-15 00:00:00 4136001 Et9kgGMDl729KT4 0 0 269.9333
## 5 2020-05-15 00:00:00 4136001 IQ2d7wF4YD8zU1Q 0 0 3177.0000
## 6 2020-05-15 00:00:00 4136001 LYwnQax7tkwH5Cb 0 0 1872.5000
## TOTAL_YIELD
## 1 2429011
## 2 1215278736
## 3 2247719577
## 4 1704250
## 5 19941526
## 6 1794958634head(plant_s_1)## DATE_TIME PLANT_ID SOURCE_KEY AMBIENT_TEMPERATURE
## 1 2020-05-15 00:00:00 4135001 HmiyD2TTLFNqkNe 25.18432
## 2 2020-05-15 00:15:00 4135001 HmiyD2TTLFNqkNe 25.08459
## 3 2020-05-15 00:30:00 4135001 HmiyD2TTLFNqkNe 24.93575
## 4 2020-05-15 00:45:00 4135001 HmiyD2TTLFNqkNe 24.84613
## 5 2020-05-15 01:00:00 4135001 HmiyD2TTLFNqkNe 24.62153
## 6 2020-05-15 01:15:00 4135001 HmiyD2TTLFNqkNe 24.53609
## MODULE_TEMPERATURE IRRADIATION
## 1 22.85751 0
## 2 22.76167 0
## 3 22.59231 0
## 4 22.36085 0
## 5 22.16542 0
## 6 21.96857 0head(plant_s_2)## DATE_TIME PLANT_ID SOURCE_KEY AMBIENT_TEMPERATURE
## 1 2020-05-15 00:00:00 4136001 iq8k7ZNt4Mwm3w0 27.00476
## 2 2020-05-15 00:15:00 4136001 iq8k7ZNt4Mwm3w0 26.88081
## 3 2020-05-15 00:30:00 4136001 iq8k7ZNt4Mwm3w0 26.68206
## 4 2020-05-15 00:45:00 4136001 iq8k7ZNt4Mwm3w0 26.50059
## 5 2020-05-15 01:00:00 4136001 iq8k7ZNt4Mwm3w0 26.59615
## 6 2020-05-15 01:15:00 4136001 iq8k7ZNt4Mwm3w0 26.51274
## MODULE_TEMPERATURE IRRADIATION
## 1 25.06079 0
## 2 24.42187 0
## 3 24.42729 0
## 4 24.42068 0
## 5 25.08821 0
## 6 25.31797 0Let’s see if any null variables exist
lapply(plant_g_1,function(x) { length(which(is.na(x)))})## $DATE_TIME
## [1] 0
##
## $PLANT_ID
## [1] 0
##
## $SOURCE_KEY
## [1] 0
##
## $DC_POWER
## [1] 0
##
## $AC_POWER
## [1] 0
##
## $DAILY_YIELD
## [1] 0
##
## $TOTAL_YIELD
## [1] 0lapply(plant_g_2,function(x) { length(which(is.na(x)))})## $DATE_TIME
## [1] 0
##
## $PLANT_ID
## [1] 0
##
## $SOURCE_KEY
## [1] 0
##
## $DC_POWER
## [1] 0
##
## $AC_POWER
## [1] 0
##
## $DAILY_YIELD
## [1] 0
##
## $TOTAL_YIELD
## [1] 0lapply(plant_s_1,function(x) { length(which(is.na(x)))})## $DATE_TIME
## [1] 0
##
## $PLANT_ID
## [1] 0
##
## $SOURCE_KEY
## [1] 0
##
## $AMBIENT_TEMPERATURE
## [1] 0
##
## $MODULE_TEMPERATURE
## [1] 0
##
## $IRRADIATION
## [1] 0lapply(plant_s_2,function(x) { length(which(is.na(x)))})## $DATE_TIME
## [1] 0
##
## $PLANT_ID
## [1] 0
##
## $SOURCE_KEY
## [1] 0
##
## $AMBIENT_TEMPERATURE
## [1] 0
##
## $MODULE_TEMPERATURE
## [1] 0
##
## $IRRADIATION
## [1] 0Look’s like we don’t have any null values!
Data Preprocessing
We have some changes to make to our data structure to make it more ideal for analysis.
-Right now we have 4 different data files, let’s combine them into one file.
-factor level data needs to be recoded
-Clean up the time stamp data- data reported in 15 minute intervals
PLANT_ID refers to the id of the plant. Let’s change PLANT_ID from character to factor
plant_g_1$PLANT_ID <- factor(plant_g_1$PLANT_ID)
plant_g_2$PLANT_ID <- factor(plant_g_2$PLANT_ID)
plant_s_1$PLANT_ID <- factor(plant_s_1$PLANT_ID)
plant_s_2$PLANT_ID <- factor(plant_s_2$PLANT_ID)SOURCE_KEY have different values for sensor and generator id- we aren’t going to be able to merge data on this factor and we can’t use this variable as a factor to compare sensor vs generator data let’s drop this and have plant_id as the main factor variable
plant_g_1$SOURCE_KEY <- NULL
plant_g_2$SOURCE_KEY <- NULL
plant_s_1$SOURCE_KEY <- NULL
plant_s_2$SOURCE_KEY <- NULLDATE_TIME reported in 15 minute intervals. Lets just aggregate our observations by day
plant_g_1$DATE <- as.Date(plant_g_1$DATE_TIME, format= '%d-%m-%Y')
plant_g_1$DATE[1:10] ## [1] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"
## [6] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"plant_g_1$DATE_TIME<- NULL# we can drop DATE_TIMEplant_g_2$DATE <- as.Date(plant_g_2$DATE_TIME, format = '%Y-%m-%d')
plant_g_2$DATE[1:10]## [1] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"
## [6] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"plant_g_2$DATE_TIME <- NULL plant_s_1$DATE <- as.Date(plant_s_1$DATE_TIME , format = '%Y-%m-%d')
plant_s_1$DATE[1:10]## [1] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"
## [6] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"plant_s_1$DATE_TIME <- NULL plant_s_2$DATE <- as.Date(plant_s_2$DATE_TIME, format = '%Y-%m-%d')
plant_s_2$DATE[1:10]## [1] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"
## [6] "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15" "2020-05-15"plant_s_2$DATE_TIME <- NULLNow that we have dates cleaned we can aggregate data by day using dplyr package
plant_g_1 <- plant_g_1 %>%
group_by(DATE, PLANT_ID) %>%
summarise_all(sum)
plant_g_1## # A tibble: 34 x 6
## # Groups: DATE [34]
## DATE PLANT_ID DC_POWER AC_POWER DAILY_YIELD TOTAL_YIELD
## <date> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 2020-05-15 4135001 5627239. 550831. 5053591. 13396793557.
## 2 2020-05-16 4135001 5806138. 568360. 6699905. 13273365620.
## 3 2020-05-17 4135001 6759595. 660975. 7804065. 14507767213.
## 4 2020-05-18 4135001 4812549. 470970. 5130290. 14520941632.
## 5 2020-05-19 4135001 5437955. 532250. 5896321. 13707398626.
## 6 2020-05-20 4135001 5375586. 525085. 5612536. 11517627080.
## 7 2020-05-21 4135001 6781068. 662742. 6627303. 9446312277.
## 8 2020-05-22 4135001 6420685. 627830. 5555931. 13989682404.
## 9 2020-05-23 4135001 7630217. 745884. 8468993. 13536007825.
## 10 2020-05-24 4135001 7160354. 699818. 8181251. 14617604912.
## # … with 24 more rowsplant_g_2 <- plant_g_2 %>%
group_by(DATE, PLANT_ID) %>%
summarise_all(sum)
plant_g_2## # A tibble: 34 x 6
## # Groups: DATE [34]
## DATE PLANT_ID DC_POWER AC_POWER DAILY_YIELD TOTAL_YIELD
## <date> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 2020-05-15 4136001 666608. 651438. 7997412. 1.35e12
## 2 2020-05-16 4136001 566840. 554253. 7234658. 1.35e12
## 3 2020-05-17 4136001 556237. 544393. 6712265. 1.36e12
## 4 2020-05-18 4136001 530774. 519013. 6259087. 1.36e12
## 5 2020-05-19 4136001 443496. 433555. 5177354. 1.31e12
## 6 2020-05-20 4136001 352374. 344661. 5764847. 1.15e12
## 7 2020-05-21 4136001 494112. 483021. 5674293. 1.26e12
## 8 2020-05-22 4136001 498711. 487412. 5897264. 1.27e12
## 9 2020-05-23 4136001 501823. 490451. 6287109. 1.26e12
## 10 2020-05-24 4136001 479294. 468609. 5635139. 1.24e12
## # … with 24 more rowsplant_s_1 <- plant_s_1 %>%
group_by(DATE,PLANT_ID) %>%
summarise_all(sum)
plant_s_1## # A tibble: 34 x 5
## # Groups: DATE [34]
## DATE PLANT_ID AMBIENT_TEMPERATURE MODULE_TEMPERATURE IRRADIATION
## <date> <fct> <dbl> <dbl> <dbl>
## 1 2020-05-15 4135001 2551. 3030. 19.0
## 2 2020-05-16 4135001 2357. 2804. 18.7
## 3 2020-05-17 4135001 2562. 3143. 22.9
## 4 2020-05-18 4135001 2290. 2670. 15.3
## 5 2020-05-19 4135001 2356. 2764. 18.0
## 6 2020-05-20 4135001 2006. 2347. 18.2
## 7 2020-05-21 4135001 1886. 2529. 23.6
## 8 2020-05-22 4135001 2547. 3118. 22.1
## 9 2020-05-23 4135001 2416. 3132. 26.1
## 10 2020-05-24 4135001 2652. 3262. 24.9
## # … with 24 more rowsplant_s_2 <- plant_s_2 %>%
group_by(DATE, PLANT_ID) %>%
summarise_all(sum)
plant_s_2## # A tibble: 34 x 5
## # Groups: DATE [34]
## DATE PLANT_ID AMBIENT_TEMPERATURE MODULE_TEMPERATURE IRRADIATION
## <date> <fct> <dbl> <dbl> <dbl>
## 1 2020-05-15 4136001 2904. 3378. 28.6
## 2 2020-05-16 4136001 2830. 3374. 23.7
## 3 2020-05-17 4136001 2859. 3324. 21.2
## 4 2020-05-18 4136001 2624. 3035. 21.5
## 5 2020-05-19 4136001 2518. 2860. 20.3
## 6 2020-05-20 4136001 2710. 3202. 26.8
## 7 2020-05-21 4136001 2789. 3339. 27.2
## 8 2020-05-22 4136001 2846. 3528. 28.5
## 9 2020-05-23 4136001 2942. 3543. 28.2
## 10 2020-05-24 4136001 2957. 3563. 27.4
## # … with 24 more rowsNow lets combine all the data into one dataframe
plant_generator <- union(plant_g_1,plant_g_2)
plant_sensor <- union(plant_s_1, plant_s_2)
plant_generator## # A tibble: 68 x 6
## # Groups: DATE [34]
## DATE PLANT_ID DC_POWER AC_POWER DAILY_YIELD TOTAL_YIELD
## <date> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 2020-05-15 4135001 5627239. 550831. 5053591. 13396793557.
## 2 2020-05-16 4135001 5806138. 568360. 6699905. 13273365620.
## 3 2020-05-17 4135001 6759595. 660975. 7804065. 14507767213.
## 4 2020-05-18 4135001 4812549. 470970. 5130290. 14520941632.
## 5 2020-05-19 4135001 5437955. 532250. 5896321. 13707398626.
## 6 2020-05-20 4135001 5375586. 525085. 5612536. 11517627080.
## 7 2020-05-21 4135001 6781068. 662742. 6627303. 9446312277.
## 8 2020-05-22 4135001 6420685. 627830. 5555931. 13989682404.
## 9 2020-05-23 4135001 7630217. 745884. 8468993. 13536007825.
## 10 2020-05-24 4135001 7160354. 699818. 8181251. 14617604912.
## # … with 58 more rowsplant_sensor## # A tibble: 68 x 5
## # Groups: DATE [34]
## DATE PLANT_ID AMBIENT_TEMPERATURE MODULE_TEMPERATURE IRRADIATION
## <date> <fct> <dbl> <dbl> <dbl>
## 1 2020-05-15 4135001 2551. 3030. 19.0
## 2 2020-05-16 4135001 2357. 2804. 18.7
## 3 2020-05-17 4135001 2562. 3143. 22.9
## 4 2020-05-18 4135001 2290. 2670. 15.3
## 5 2020-05-19 4135001 2356. 2764. 18.0
## 6 2020-05-20 4135001 2006. 2347. 18.2
## 7 2020-05-21 4135001 1886. 2529. 23.6
## 8 2020-05-22 4135001 2547. 3118. 22.1
## 9 2020-05-23 4135001 2416. 3132. 26.1
## 10 2020-05-24 4135001 2652. 3262. 24.9
## # … with 58 more rowsdf <- merge(plant_generator,plant_sensor, by = c('PLANT_ID','DATE'))Data
DATE_TIME(date time): Refers to the date_time in 15 minute intervals
PLANT_ID(factor): Refers to the specific plant ID- there are only two plants that have been sampled
AMBIENT_TEMPERATURE(num): Temperature at the plant
MODULE_TEMPERATURE(num): Temperature of the sensor
IRRADIATION(num): Amount of solar IRRADIATION in 15 minute intervals. Solar irradiation refers to the conversion of solar light to solar energy.
DC_POWER(num): Amount of direct current power generated in 15 minute intervals
AC_POWER(num): Amount of alternating current power generated in 15 minute intervals
DAILY_YIELD(num): Cumulative sum of power generated at that point in the day
TOTAL_YIELD(num): Total yield for that inverter up until that point
Review the dataframe and it’s structure
df## PLANT_ID DATE DC_POWER AC_POWER DAILY_YIELD TOTAL_YIELD
## 1 4135001 2020-05-15 5627239.1 550831.0 5053591 1.339679e+10
## 2 4135001 2020-05-16 5806137.5 568359.8 6699905 1.327337e+10
## 3 4135001 2020-05-17 6759594.5 660975.4 7804065 1.450777e+10
## 4 4135001 2020-05-18 4812548.5 470969.7 5130290 1.452094e+10
## 5 4135001 2020-05-19 5437954.9 532250.5 5896321 1.370740e+10
## 6 4135001 2020-05-20 5375585.8 525084.6 5612536 1.151763e+10
## 7 4135001 2020-05-21 6781068.1 662742.4 6627303 9.446312e+09
## 8 4135001 2020-05-22 6420684.5 627830.1 5555931 1.398968e+10
## 9 4135001 2020-05-23 7630217.2 745884.3 8468993 1.353601e+10
## 10 4135001 2020-05-24 7160353.9 699817.8 8181251 1.461760e+10
## 11 4135001 2020-05-25 7898965.1 771576.2 9053215 1.427449e+10
## 12 4135001 2020-05-26 7052704.9 689483.8 4376113 1.437069e+10
## 13 4135001 2020-05-27 5985527.1 585707.9 5127007 1.424149e+10
## 14 4135001 2020-05-28 7501395.2 733119.5 7578132 1.376566e+10
## 15 4135001 2020-05-29 7295130.2 713110.6 6103425 1.036161e+10
## 16 4135001 2020-05-30 6502312.9 636043.2 7050152 1.471706e+10
## 17 4135001 2020-05-31 5378552.5 525939.2 6214020 1.469282e+10
## 18 4135001 2020-06-01 5210134.0 509691.5 6387988 1.474426e+10
## 19 4135001 2020-06-02 6631810.9 648667.6 6224743 1.459238e+10
## 20 4135001 2020-06-03 6732591.3 658508.4 7677981 1.464635e+10
## 21 4135001 2020-06-04 7321031.5 715775.2 6091402 1.435999e+10
## 22 4135001 2020-06-05 6898473.8 674574.2 6384127 1.458579e+10
## 23 4135001 2020-06-06 5730938.5 560332.5 5076817 1.439118e+10
## 24 4135001 2020-06-07 6876444.2 672139.5 7747108 1.483665e+10
## 25 4135001 2020-06-08 7470115.1 730087.5 8505252 1.485356e+10
## 26 4135001 2020-06-09 7234008.9 707237.5 8260297 1.487087e+10
## 27 4135001 2020-06-10 5784039.5 565937.5 6679794 1.488627e+10
## 28 4135001 2020-06-11 5045678.6 494174.9 5538094 1.489873e+10
## 29 4135001 2020-06-12 5222353.9 511289.7 5848817 1.491091e+10
## 30 4135001 2020-06-13 7593776.3 742032.7 8705923 1.492604e+10
## 31 4135001 2020-06-14 6350494.6 621509.3 7240643 1.494235e+10
## 32 4135001 2020-06-15 6055535.9 592483.9 7137433 1.495713e+10
## 33 4135001 2020-06-16 5572501.3 545506.7 6512585 1.497068e+10
## 34 4135001 2020-06-17 5317779.8 520383.5 6138883 1.467137e+10
## 35 4136001 2020-05-15 666607.6 651437.7 7997412 1.347430e+12
## 36 4136001 2020-05-16 566839.8 554253.5 7234658 1.346965e+12
## 37 4136001 2020-05-17 556236.9 544393.0 6712265 1.357864e+12
## 38 4136001 2020-05-18 530773.7 519012.6 6259087 1.361871e+12
## 39 4136001 2020-05-19 443495.8 433554.7 5177354 1.314653e+12
## 40 4136001 2020-05-20 352374.4 344661.4 5764847 1.146138e+12
## 41 4136001 2020-05-21 494112.3 483021.4 5674293 1.258768e+12
## 42 4136001 2020-05-22 498711.3 487411.9 5897264 1.274881e+12
## 43 4136001 2020-05-23 501823.3 490450.5 6287109 1.258321e+12
## 44 4136001 2020-05-24 479293.5 468609.4 5635139 1.236102e+12
## 45 4136001 2020-05-25 582787.3 569576.3 6996642 1.247754e+12
## 46 4136001 2020-05-26 576620.1 563483.2 6481991 1.219494e+12
## 47 4136001 2020-05-27 445436.7 435466.2 5784824 1.148820e+12
## 48 4136001 2020-05-28 499034.0 487742.9 5866414 1.256704e+12
## 49 4136001 2020-05-29 496059.2 485377.1 6808404 1.291878e+12
## 50 4136001 2020-05-30 614530.6 600856.5 7154658 1.353977e+12
## 51 4136001 2020-05-31 556847.6 544366.1 7125460 1.350929e+12
## 52 4136001 2020-06-01 372059.0 363681.3 5135112 1.339304e+12
## 53 4136001 2020-06-02 519492.0 508269.6 5840944 1.310165e+12
## 54 4136001 2020-06-03 414845.2 406045.1 5351371 1.333943e+12
## 55 4136001 2020-06-04 474970.4 464789.5 5967317 1.358949e+12
## 56 4136001 2020-06-05 518707.5 507337.9 7945888 1.362251e+12
## 57 4136001 2020-06-06 527117.1 515131.9 7721987 1.339788e+12
## 58 4136001 2020-06-07 473278.9 462528.8 7404470 1.328888e+12
## 59 4136001 2020-06-08 604333.9 590644.6 8970222 1.361305e+12
## 60 4136001 2020-06-09 554027.1 541913.6 8804847 1.355549e+12
## 61 4136001 2020-06-10 393589.8 385086.4 6741997 1.318146e+12
## 62 4136001 2020-06-11 342752.9 335847.8 5529623 1.339452e+12
## 63 4136001 2020-06-12 411233.9 402905.0 6011759 1.350843e+12
## 64 4136001 2020-06-13 455305.8 445507.8 6743320 1.325963e+12
## 65 4136001 2020-06-14 505911.5 495073.5 7827889 1.362168e+12
## 66 4136001 2020-06-15 410998.9 402322.1 6926075 1.362414e+12
## 67 4136001 2020-06-16 480810.1 470830.4 7089666 1.340767e+12
## 68 4136001 2020-06-17 380211.2 372436.3 4187174 1.346798e+12
## AMBIENT_TEMPERATURE MODULE_TEMPERATURE IRRADIATION
## 1 2551.067 3030.216 19.03701
## 2 2356.687 2803.579 18.65169
## 3 2561.926 3143.082 22.93138
## 4 2289.690 2670.177 15.26649
## 5 2356.436 2764.440 18.04486
## 6 2006.143 2346.567 18.24554
## 7 1886.155 2528.707 23.55617
## 8 2546.563 3117.973 22.11912
## 9 2415.566 3132.166 26.10665
## 10 2652.011 3261.940 24.93718
## 11 2612.175 3315.260 27.23337
## 12 2582.828 3213.423 24.25059
## 13 2576.205 3112.348 20.53757
## 14 2569.563 3216.305 26.03238
## 15 2085.899 2868.066 24.79566
## 16 2399.157 2958.337 21.87505
## 17 2445.370 2895.428 17.62546
## 18 2378.833 2780.264 17.64924
## 19 2339.992 2827.022 21.48365
## 20 2355.589 2849.816 21.92771
## 21 2427.473 2997.276 24.67097
## 22 2387.580 2935.926 23.19266
## 23 2327.746 2765.066 19.52688
## 24 2401.545 3023.798 24.40237
## 25 2442.362 3035.705 25.31553
## 26 2452.391 3025.511 24.75467
## 27 2376.237 2803.444 19.23229
## 28 2342.727 2676.505 15.53371
## 29 2310.948 2648.240 16.30155
## 30 2358.406 2926.178 25.38935
## 31 2343.638 2824.484 21.12822
## 32 2383.432 2873.070 19.76881
## 33 2393.177 2837.334 17.97913
## 34 2326.054 2723.956 16.98851
## 35 2903.769 3378.152 28.55906
## 36 2829.947 3373.758 23.67657
## 37 2858.891 3324.166 21.23360
## 38 2624.323 3035.337 21.49578
## 39 2517.563 2860.078 20.34532
## 40 2710.370 3201.587 26.78687
## 41 2789.324 3339.149 27.19118
## 42 2846.262 3527.813 28.53584
## 43 2942.362 3543.355 28.15998
## 44 2957.371 3563.189 27.42604
## 45 2958.569 3510.436 26.55693
## 46 2882.687 3434.776 27.23467
## 47 2918.490 3555.311 27.43194
## 48 2892.485 3459.237 28.13703
## 49 2854.501 3313.966 23.23721
## 50 2836.672 3227.572 23.82700
## 51 2731.323 3177.390 19.20396
## 52 2423.169 2706.907 13.43026
## 53 2601.831 3156.786 23.74862
## 54 2482.750 2809.381 16.61464
## 55 2525.274 2959.750 20.18278
## 56 2599.906 3100.854 22.36660
## 57 2668.925 3153.679 25.96374
## 58 2674.153 3225.085 25.03494
## 59 2735.361 3293.972 27.03844
## 60 2700.185 3164.197 23.83802
## 61 2624.123 2959.345 18.57632
## 62 2450.007 2615.839 11.27796
## 63 2369.608 2603.222 13.10297
## 64 2507.226 2917.908 20.69017
## 65 2593.900 3032.624 22.03363
## 66 2549.529 2879.638 17.76505
## 67 2531.510 2840.630 15.84592
## 68 2385.809 2560.189 11.94076str(df)## 'data.frame': 68 obs. of 9 variables:
## $ PLANT_ID : Factor w/ 2 levels "4135001","4136001": 1 1 1 1 1 1 1 1 1 1 ...
## $ DATE : Date, format: "2020-05-15" "2020-05-16" ...
## $ DC_POWER : num 5627239 5806138 6759595 4812549 5437955 ...
## $ AC_POWER : num 550831 568360 660975 470970 532250 ...
## $ DAILY_YIELD : num 5053591 6699905 7804065 5130290 5896321 ...
## $ TOTAL_YIELD : num 1.34e+10 1.33e+10 1.45e+10 1.45e+10 1.37e+10 ...
## $ AMBIENT_TEMPERATURE: num 2551 2357 2562 2290 2356 ...
## $ MODULE_TEMPERATURE : num 3030 2804 3143 2670 2764 ...
## $ IRRADIATION : num 19 18.7 22.9 15.3 18 ...head(df)## PLANT_ID DATE DC_POWER AC_POWER DAILY_YIELD TOTAL_YIELD
## 1 4135001 2020-05-15 5627239 550831.0 5053591 13396793557
## 2 4135001 2020-05-16 5806138 568359.8 6699905 13273365620
## 3 4135001 2020-05-17 6759595 660975.4 7804065 14507767213
## 4 4135001 2020-05-18 4812549 470969.7 5130290 14520941632
## 5 4135001 2020-05-19 5437955 532250.5 5896321 13707398626
## 6 4135001 2020-05-20 5375586 525084.6 5612536 11517627080
## AMBIENT_TEMPERATURE MODULE_TEMPERATURE IRRADIATION
## 1 2551.067 3030.216 19.03701
## 2 2356.687 2803.579 18.65169
## 3 2561.926 3143.082 22.93138
## 4 2289.690 2670.177 15.26649
## 5 2356.436 2764.440 18.04486
## 6 2006.143 2346.567 18.24554Basic statistics
summary(df)## PLANT_ID DATE DC_POWER AC_POWER
## 4135001:34 Min. :2020-05-15 Min. : 342753 Min. :335848
## 4136001:34 1st Qu.:2020-05-23 1st Qu.: 498048 1st Qu.:484788
## Median :2020-05-31 Median :2739578 Median :543140
## Mean :2020-05-31 Mean :3429043 Mean :551531
## 3rd Qu.:2020-06-09 3rd Qu.:6441092 3rd Qu.:639199
## Max. :2020-06-17 Max. :7898965 Max. :771576
## DAILY_YIELD TOTAL_YIELD AMBIENT_TEMPERATURE MODULE_TEMPERATURE
## Min. :4187174 Min. :9.446e+09 Min. :1886 Min. :2347
## 1st Qu.:5826914 1st Qu.:1.459e+10 1st Qu.:2382 1st Qu.:2826
## Median :6497288 Median :5.806e+11 Median :2528 Median :3025
## Mean :6613936 Mean :6.631e+11 Mean :2540 Mean :3026
## 3rd Qu.:7281600 3rd Qu.:1.339e+12 3rd Qu.:2681 3rd Qu.:3218
## Max. :9053215 Max. :1.362e+12 Max. :2959 Max. :3563
## IRRADIATION
## Min. :11.28
## 1st Qu.:18.63
## Median :22.08
## Mean :21.84
## 3rd Qu.:25.11
## Max. :28.56EDA:Visualize & Understand data
Let’s start by look at distributions & outliers of all variables
v1 <- ggdensity(df$DAILY_YIELD,fill = 'skyblue4', main = 'Distribution of daily yield')
v2 <- ggqqplot(df$DAILY_YIELD, col='springgreen4')
v3 <- ggboxplot(df$DAILY_YIELD, fill = 'yellow3', col= "snow4", main ='Daily yield outliers')
grid.arrange(v1, v2,v3, nrow=3)
Daily yield approx normally distributed with some possibly extreme values & appears to be linear
v4 <- ggdensity(df$AC_POWER, fill = 'skyblue4', main = 'Distribution of alternating current')
v5 <- ggqqplot(df$AC_POWER, col='springgreen4')
v6 <- ggboxplot(df$AC_POWER, fill = 'yellow3', col= "snow4", main ='Anlternating current outliers')
grid.arrange(v4,v5,v6, nrow=3)
AC_POWER is approaching normality & appears to be linear
v7 <- ggdensity(df$DC_POWER, fill = 'skyblue4', main = 'Distribution of direct current')
v8 <- ggqqplot(df$DC_POWER, col='springgreen4')
v9 <- ggboxplot(df$DC_POWER, fill = 'yellow3', col= "snow4", main ='Direct current outliers')
grid.arrange(v7, v8, v9, nrow=3)
DC_POWER appearing bimodal & possibly s curve
v10 <- ggdensity(df$TOTAL_YIELD, fill = 'skyblue4', main = 'Distribution of total yield')
v11 <- ggqqplot(df$TOTAL_YIELD, col='springgreen4')
v12 <- ggboxplot(df$TOTAL_YIELD, fill = 'yellow3', col= "snow4", main ='total yield outliers')
grid.arrange(v10, v11, v12, nrow=3)
TOTAL_YIELD appearing bimodel and possible s curve
v13 <- ggdensity(df$AMBIENT_TEMPERATURE, fill = 'skyblue4', main = 'Distribution of ambient temperature')
v14 <- ggqqplot(df$AMBIENT_TEMPERATURE, col='springgreen4')
v15 <- ggboxplot(df$AMBIENT_TEMPERATURE, fill = 'yellow3', col= "snow4", main ='Ambient temperature outliers')
grid.arrange(v13, v14, v15, nrow=3)
AMBIENT_TEMPERATURE is linear, could be approaching normal, not extreme outliers
v16 <- ggdensity(df$MODULE_TEMPERATURE, fill = 'skyblue4', main = 'Distribution of module temperature')
v17 <- ggqqplot(df$MODULE_TEMPERATURE, col='springgreen4')
v18 <- ggboxplot(df$MODULE_TEMPERATURE, fill = 'yellow3', col= "snow4", main ='Module temperature outliers')
grid.arrange(v16,v17,v18, nrow=3)
MODULE_TEMPERATURE linear, approaching normal
v19 <- ggdensity(df$IRRADIATION, fill = 'skyblue4', main = 'Distribution of irradiation')
v20 <- ggqqplot(df$IRRADIATION, col='springgreen4')
v21 <- ggboxplot(df$IRRADIATION, fill = 'yellow3', col= "snow4", main ='Irradiation outliers')
grid.arrange(v19, v20, v21, nrow=3)
IRRADIATION linear
Looking at each variables distributions gives us a sense of what variables are normally distributed and linear- giving us a better sense of what kind of possible tests and questions we want to ask about our data
Here are a few questions I have and plan to explore during this EDA
Which power plant performs better?
Are there significant differences between types of power?
How does irradiation relate to different energy
Does a relationship between temp, irradiation, and energy exist?
Are there any relevant predictors of daily yield?
keeping in mind that DC_power, and total_yielded_power have very non linear and normal distributions I will use the below sections to address and answer all these questions as well as any new questions that arise
Q1: Which power plant performs better?
Let’s start by looking at the different power plants
boxplot(df$DAILY_YIELD~df$PLANT_ID, main= 'Plant 1 vs. Plant 2:Examining Outliers', xlab='plant id', ylab='daily yield',col= c('springgreen4','skyblue4'))
What is the average daily yield per plant?
dy_means <- aggregate(df$DAILY_YIELD, by=list(df$PLANT_ID), FUN = mean)
dy_means## Group.1 x
## 1 4135001 6667357
## 2 4136001 6560514barplot(dy_means$x, names.arg = dy_means$Group.1, col= c('springgreen4','skyblue4'))
title("Mean daily energy yielded")
There does not appear to be a large difference between the daily energy yielded by plant. Let’s run a test and see if there are mean differences
summary(aov(df$DAILY_YIELD~df$PLANT_ID))## Df Sum Sq Mean Sq F value Pr(>F)
## df$PLANT_ID 1 1.941e+11 1.941e+11 0.15 0.7
## Residuals 66 8.545e+13 1.295e+12There is no significant difference between energy yielded between plants.
What about ac_power?
ac_mean <- aggregate(df$AC_POWER, by= list(df$PLANT_ID), FUN = mean)
ac_mean## Group.1 x
## 1 4135001 622648.8
## 2 4136001 480412.5barplot(ac_mean$x, names.arg=ac_mean$Group.1,col= c('springgreen4','skyblue4'))
title("Mean daily alternating current energy yielded ")
Each plant seems to yield a difference amount of alternating current energy
Let’s see if these differences are significant?
summary(aov(df$AC_POWER~df$PLANT_ID))## Df Sum Sq Mean Sq F value Pr(>F)
## df$PLANT_ID 1 3.439e+11 3.439e+11 52.04 6.74e-10 ***
## Residuals 66 4.362e+11 6.609e+09
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1As suspected the mean daily alternating current yielded significantly differs between each plant
Let’s explore DC_POWER
dc_mean <- aggregate(df$DC_POWER, by= list(df$PLANT_ID), FUN= mean)
dc_mean## Group.1 x
## 1 4135001 6366872.9
## 2 4136001 491212.6barplot(dc_mean$x, names.arg = dc_mean$Group.1,col= c('springgreen4','skyblue4'))
title("Mean daily direct current energy yielded ")
Similar to AC_POWER, each plant seems to generate different amounts of direct current on a daily basis
Let’s run a t test to seem if the differences are significant
plant_1 <- df[df$PLANT_ID == 4135001,]
plant_2 <- df[df$PLANT_ID != 4135001,]
t.test(plant_1$DC_POWER,plant_2$DC_POWER)##
## Welch Two Sample t-test
##
## data: plant_1$DC_POWER and plant_2$DC_POWER
## t = 38.538, df = 33.51, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 5565646 6185675
## sample estimates:
## mean of x mean of y
## 6366872.9 491212.6We see significant differences between dc for each plant. Overall there is a difference between alternating & direct current production for each plant.However, we do not see significant difference in how much power total power is yielded per day.
Q2: Are there significant differences between types of power?
What about differences between AC & DC power regardless of power plant?
# Looks like a difference between means.
t.test(df$AC_POWER,df$AC_POWER)##
## Welch Two Sample t-test
##
## data: df$AC_POWER and df$AC_POWER
## t = 0, df = 134, p-value = 1
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -36600.73 36600.73
## sample estimates:
## mean of x mean of y
## 551530.6 551530.6We do not see a signifcant differences between alternating and direct current.
It looks like the differences are at the factor level or the plants. Plant 1
to perform signifcantly better for producing direct and alternating current
Next let’s investigate eraddation levels
what is the average eradation level?
mean(df$IRRADIATION)## [1] 21.83796What’s the relationship of irradiation and time?
plot(df$DATE,df$IRRADIATION, main = 'Daily Irradation Levels', xlab='Day',ylab='Irradation level', pch= 19, col='springgreen4')
We don’t see a clear relationship between time & irradation levels.
It’s possible a relationship exists over longer periods of time For example
month over month, but a limitation of this data is sample is only 34 days.
Q3: How does irradiation relate to different energy
plot(df$IRRADIATION,df$DAILY_YIELD, main= 'Relationship between daily
yielded power & Irradation', xlab= 'Irradation', ylab = 'Daily yielded power',pch= 19, col='springgreen4')
This relationship is moderately linear, with a few apparent outliers.
plot(df$IRRADIATION,df$AC_POWER, main= 'Relationship between alternating
current power & Irradation', xlab= 'Irradation', ylab = 'Alternating power current',pch= 19, col='springgreen4')
We see a somewhat linear, possible curve relationship.
how does irradation relate to different types of temperature?
plot(df$IRRADIATION,df$AMBIENT_TEMPERATURE, main= 'Relationship between ambient
temperature and irradation', xlab= 'Irradiation', ylab = ' Ambient Temperature',
pch= 19, col='springgreen4')
We see a slight curvlinear relationship, that may benefit in a transformation
plot(df$IRRADIATION,df$MODULE_TEMPERATURE, main= 'Relationship between module
temperature and irradation', xlab= 'Irradiation', ylab = ' Module Temperature',
pch= 19, col='springgreen4')
We also so a linear relationship between irradation and module temperature
Let’s look at other possible relationships between variables
plot(df$AMBIENT_TEMPERATURE,df$MODULE_TEMPERATURE, main= 'Relationship between module
temperature and ambient temperature', xlab= 'Ambient temperature', ylab = ' Module Temperature',
pch= 19, col='springgreen4')
#### Unsurprisingly we see a strong linear relationship between temperature.
plot(df$MODULE_TEMPERATURE,df$AC_POWER, main= 'Relationship between module
temperature and alternating current', xlab= 'Ambient temperature', ylab = 'Alternating current',
pch= 19, col='springgreen4')
plot(df$MODULE_TEMPERATURE,df$DAILY_YIELD, main= 'Relationship between module
temperature and daily yield', xlab= 'Ambient temperature', ylab = 'Daily yield',
pch= 19, col='springgreen4')
#### We see a pretty similar relationship for energy yields and ambient temperature
plot(df$AMBIENT_TEMPERATURE,df$MODULE_TEMPERATURE, main= 'Relationship between module
temperature and ambient temperature', xlab= 'Ambient temperature', ylab = ' Module Temperature',
pch= 19, col='springgreen4') #### Let’s look at the correlation between variables
df_cor<- cor(df[,unlist(lapply(df, is.numeric))])
library(corrplot)## corrplot 0.84 loadedcol<- colorRampPalette(c('yellow3','springgreen4','skyblue4'))(20)
corrplot(df_cor, method= 'square', type='upper', col=col,tl.col="snow4", tl.srt=45)
dvs: ac_power, daily_yield, ambient_temp and module_temp correlates?
ac power & module & ambient temp have low correlations r< .30
Q4:Does a relationship between temp, irradiation, and energy exist?
Through our EDA we saw irradiation has a linear relationship with a few variables. Can we use temp and energy yielded to predict irradation levels?
To deal with multicorrelates we will search procedures- step forward to help identify the best model
Let’s start with building a multiple linear regression model with all the variables
we investigated with irradiation
irridation <- lm(IRRADIATION ~AC_POWER+MODULE_TEMPERATURE+DAILY_YIELD+AMBIENT_TEMPERATURE, data=df)
irridation##
## Call:
## lm(formula = IRRADIATION ~ AC_POWER + MODULE_TEMPERATURE + DAILY_YIELD +
## AMBIENT_TEMPERATURE, data = df)
##
## Coefficients:
## (Intercept) AC_POWER MODULE_TEMPERATURE
## -1.099e+01 -1.181e-06 2.575e-02
## DAILY_YIELD AMBIENT_TEMPERATURE
## 4.989e-07 -1.879e-02summary(irridation)##
## Call:
## lm(formula = IRRADIATION ~ AC_POWER + MODULE_TEMPERATURE + DAILY_YIELD +
## AMBIENT_TEMPERATURE, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2124 -1.1311 -0.1914 0.8213 4.3281
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.099e+01 3.030e+00 -3.627 0.000576 ***
## AC_POWER -1.181e-06 3.401e-06 -0.347 0.729500
## MODULE_TEMPERATURE 2.575e-02 2.591e-03 9.938 1.59e-14 ***
## DAILY_YIELD 4.989e-07 2.218e-07 2.249 0.027990 *
## AMBIENT_TEMPERATURE -1.879e-02 3.280e-03 -5.730 3.04e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.656 on 63 degrees of freedom
## Multiple R-squared: 0.8632, Adjusted R-squared: 0.8545
## F-statistic: 99.41 on 4 and 63 DF, p-value: < 2.2e-16The model is significant p <.01 overall and yields R-squared of 85%, and a relatively lower residual standard error.
y = -1.099 -1.181(ac_power) + 2.575(module_temperature) + 4.989(daily_yield) - 1.879(ambient_temperature)
Further investigation of the model that daily yield ,module & ambient temperature are significant
predictors.
Let’s use search procedures to find the best version of this model.
using the olsrr package we can explore different search procedures
we’ll emplore step forward for ease
ols_step_forward_p(irridation)##
## Selection Summary
## ------------------------------------------------------------------------------------
## Variable Adj.
## Step Entered R-Square R-Square C(p) AIC RMSE
## ------------------------------------------------------------------------------------
## 1 MODULE_TEMPERATURE 0.6567 0.6515 94.1169 324.9532 2.5631
## 2 AMBIENT_TEMPERATURE 0.8507 0.8461 6.7895 270.3579 1.7036
## 3 DAILY_YIELD 0.8630 0.8565 3.1206 266.5097 1.6446
## ------------------------------------------------------------------------------------Using step forward procedures we see that the best predictors of irridation are module temperature, ambient temperature and daily yielded energy.
A few things to consider while looking at the selection summary R squared refers to the amount of variability that can be attributed to the predictor(irridation). We have decent r squared= with daily yiled & ambient temp
irridation_best <- lm(IRRADIATION~MODULE_TEMPERATURE+AMBIENT_TEMPERATURE+DAILY_YIELD, data=df)
irridation_best##
## Call:
## lm(formula = IRRADIATION ~ MODULE_TEMPERATURE + AMBIENT_TEMPERATURE +
## DAILY_YIELD, data = df)
##
## Coefficients:
## (Intercept) MODULE_TEMPERATURE AMBIENT_TEMPERATURE
## -1.161e+01 2.510e-02 -1.792e-02
## DAILY_YIELD
## 4.615e-07summary(irridation_best)##
## Call:
## lm(formula = IRRADIATION ~ MODULE_TEMPERATURE + AMBIENT_TEMPERATURE +
## DAILY_YIELD, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2513 -1.0743 -0.1376 0.8855 4.3400
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.161e+01 2.422e+00 -4.795 1.01e-05 ***
## MODULE_TEMPERATURE 2.510e-02 1.760e-03 14.257 < 2e-16 ***
## AMBIENT_TEMPERATURE -1.792e-02 2.106e-03 -8.510 4.08e-12 ***
## DAILY_YIELD 4.615e-07 1.925e-07 2.397 0.0194 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.645 on 64 degrees of freedom
## Multiple R-squared: 0.863, Adjusted R-squared: 0.8565
## F-statistic: 134.3 on 3 and 64 DF, p-value: < 2.2e-16We see that daily_yield, module temp and ambient temp are the best predictors of irridation levels
y = -1.161 + 2.51(module_temperature) + 4.615(daily_yield) - 1.79(ambient_temperature)
Let’s investigate assumptions of this linear regression and this model by looking at residuals
plot(irridation_best)
Looking at the residual vs fitted plot will help us understand if our model is appropriate for glm.
The residuals are random around the 0 line suggesting that the relationship is reasonably linear.
The residuals roughly form a horizontal band around the 0 line, suggesting that the variances of the error terms are equal.
We do see some residuals that stand out- suggesting that outliers do exist.
Looking at the QQ plot we see that the model roughly fits a straight line
Scale location plots indicate spread of points across the predicted values range.
Ideally there should be a horizontal line, indicating homoscedasticity.
This model is homoscedastic, meaning it has an uniform variance and it becomes heteroscedastic around 23
Residuals vs. leverage
We aren’t seeing any points that fall within cook’s distance, which suggest
there are not observations that have high leverage or are potientially influencing
our model
Overall this model meets the assumptions of linear regression!
Q5: Are there any relevant predictors of daily yield?
Next see if we can predict total energy from the type energy types
Let’s examine the relationship between energy & Alternating current
plot(df$DAILY_YIELD,df$AC_POWER, main= 'Relationship between daily yield &
alternating current', xlab= 'Daily Energy Yield', ylab= 'Daily Alternating Current Yielded',
pch= 19, col='springgreen4')
There is weak linear relationship, perhaps treating outliers will give us a better relationship
plot(df$DAILY_YIELD, df$DC_POWER, main= 'Relationship between daily yield &
direct current', xlab= 'Daily Energy Yield', ylab= 'Daily Direct Current Yielded' ,
pch= 19, col='springgreen4' )
There appears to be a linear relationship with a large amount of outliers
we may not be able to use direct current as a linear predictor of daily yield, but we can still look at AC_POWER
energy <- lm(df$DAILY_YIELD~df$AC_POWER)
energy ##
## Call:
## lm(formula = df$DAILY_YIELD ~ df$AC_POWER)
##
## Coefficients:
## (Intercept) df$AC_POWER
## 3.593e+06 5.478e+00summary(energy)##
## Call:
## lm(formula = df$DAILY_YIELD ~ df$AC_POWER)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2993490 -549610 -9637 631893 2243591
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.593e+06 6.177e+05 5.816 1.92e-07 ***
## df$AC_POWER 5.478e+00 1.099e+00 4.982 4.80e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 971100 on 66 degrees of freedom
## Multiple R-squared: 0.2733, Adjusted R-squared: 0.2623
## F-statistic: 24.82 on 1 and 66 DF, p-value: 4.797e-06Overall the model is insignificant, has a low R squared, and an extremely high residual standard error suggesting this model is not a great fit for linear regression.
Summary
Overall the data yielded some interesting findings as we explored the data. We were able to address these questions
Which power plant performs better? Power plant 1(4135001) performs better on average than plant 2(4136001). We did find a significant difference in how much direct current and the alternating current was yielded on a daily basis per plant. However, there is no evidence to support that there was a significant difference between plants for overall energy yielded.
Are there significant differences between types of power? There were no significant differences in how much alternating vs. direct current is created on average.
How does irradiation relate to different energy We see a positive linear relationship between irradiation levels and alternating current. This suggests that higher irradiation levels yield higher alternating current power produced. However, we did not see much of a relationship between direct current and irradiation.
Does a relationship between temp, irradiation, and energy exist? We were able to find that irradiation levels can be predicted by different variables such as temperature, and total energy yielded. This is an interesting finding because irradiation is the conversion of solar light to solar energy. More irradiance allows us to convert and yield more energy. We can use this model to better understand how much irradiation we need to yield a certain amount of energy and identify the best conditions for the conversion of solar to solar energy. If we have target energy yield goals we can use this model to identify what irradiation conditions are needed to meet those goals.
Are there any relevant predictors of daily yield? Unfortunately, we were not able to find any significant predictors of daily yield. We did see a slight positive relationship between alternating current and daily yield, which suggests that higher alternating current output results in higher energy yielded overall.
Limitations We have a limited amount of observations (34 days), and we would except changes to things like the overall distributions to become more normalized as well as identify long term trends such as how seasons impact energy produced. Additionally other geospatial data would be interesting to incorporate.